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Unformatted text preview: ISyE 3232 Stochastic Manufacturing and Service Systems Spring 2011 J. Dai and H. Ayhan Solutions to Homework 12 1. For all the subproblem below, the state space will always be { , 1 , 2 , 3 } . (a) The transition diagram is as the following Solve the stationary distribution using “cuts”, we get π = (1 / 15 , 2 / 15 , 4 / 15 , 8 / 15) So the throughput is λ eff = 2(1 π 3 ) = 14 / 15. To find the average waiting time, we use Little’s law. Note that L = 1 π 2 + 2 π 3 = 20 / 15, so W = L λ eff = 4 / 7 . (b) The transition diagram is as the following Solve the stationary distribution using “cuts”, we get π = (1 / 7 , 2 / 7 , 2 / 7 , 2 / 7) So the throughput is λ eff = 2(1 π 3 ) = 4 / 7. To find the average waiting time, we use Little’s law. Note that L = 1 π 3 = 7 / 2, so W = L λ eff = 1 / 5 . (c) The transition diagram is as the following 1 Solve the stationary distribution using “cuts”, we get π = (3 / 19 , 6 / 19 , 6 / 19 , 4 / 19) So the throughput is λ eff = 2(1 π...
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 Spring '07
 Billings
 Probability theory, Simultaneous Equations, Exponential distribution, Elementary algebra, average waiting time

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